IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Project appraisal
A project has cashflows of -₹100 at time 0, +₹230 at time 1 and -₹132 at time 2 (₹ lakh). Which statement about its internal rate of return is correct?
There are two IRRs, 10% and 20%. The cashflow signs change twice (-, +, -), so the equation of value is a quadratic in v with two positive roots. Both 10% and 20% give a net present value of zero, so no unique IRR exists.
- AThere are exactly two IRRs, 10% and 20%Correct
- BThere is a unique IRR of 15%
- CThere is a unique IRR of 10%
- DThere is a unique IRR of 20%
- There is no real IRR
Explanation
The equation -100 + 230v - 132v^2 = 0 is a quadratic in v with two roots. At i = 10%: -100 + 209.09 - 109.09 = 0. At i = 20%: -100 + 191.67 - 91.67 = 0. Since the cashflow signs change twice, multiple IRRs can occur, so 15% (the average) is not a root: at 15% the value is -100 + 200 - 99.81 = 0.19, not zero.
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